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Trying to grasp the idea

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Liquid flows through a 4.0 cm diameter pipe at 1.0 m/s. there is a 2.0 cm diameter restriction in the line. What is the liquids velocity in this restriction?

    2. Relevant equations



    3. The attempt at a solution
    I know that solution is 4.0 m/s but in dont know how to get there. Thank you
     
  2. jcsd
  3. Apr 19, 2009 #2

    Astronuc

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    Staff Emeritus
    Science Advisor

    The concept one is concerned with here is continuity. For an incompressible fluid, the mass flow (rate) into a control volume must equal the mass flow (rate) out, otherwise mass would accumulate or decrease in the volume.

    The mass flow rate is given by ρVA, where ρ is the fluid density, V is the mean (average) velocity and A is the cross-sectional area.

    So we have ρVA(in) = ρVA(out), or ρVA(in) - ρVA(out) = 0, i.e. no net gain or loss of fluid (mass).

    Now if ρ(in) = ρ(out), then the continuity equation becomes, V(in)A(in) = V(out)A(out).

    Try apply this to given problem.
     
  4. Apr 19, 2009 #3

    fluidistic

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    Gold Member

    Re: Trying to grasp the idea of velocity!

    There is a principle that states Av=constant, where A is the area of the fluid's path at a given time and v is the velocity.
    Hence the answer is not 4.0 m/s, unless I'm wrong.
     
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